Security firm G4S will be considered for government business again after it was barred from bidding for new contracts in a row about overcharging.
The company agreed to repay £109m after an audit found it charged too much for providing electronic prisoner tags.
The Serious Fraud Office is examining G4S and Serco over the contracts.
But the Cabinet Office said G4S had taken "positive steps" to change its practices and engaged "constructively" with the government.
The firm has not bid for any government work since the Ministry of Justice started an investigation a year ago into its supply of electronic monitoring tags for prisoners in England and Wales since 2005.
After an audit by accountancy firm PricewaterhouseCoopers, it emerged that G4S - which insisted it had asked for the review itself - and Serco had overcharged the government by "tens of millions of pounds".
'Corporate renewal plan'
The chief executive of G4S apologised to MPs last November amid claims that the company had charged for the tagging of prisoners who were either in jail, dead or abroad.
G4S also made the headlines in 2012 after it failed to provide all its contracted security guards for the London 2012 Olympics.
This prompted extra military personnel to be called in to fill the gap and left the firm with losses of £88m.
The Cabinet Office said G4S had taken steps to address weakness in its operations and its "corporate renewal plan represented the right direction of travel to meet our expectations as a customer".
After an independent review, the company will be able to bid again for government work, although this will be dependent on it implementing changes in a "full and timely manner".
Cabinet Office minister Francis Maude said: "The changes G4S has already made and its commitment to go further over coming months are positive steps that the government welcomes."
Mr Maude said the government would continue to monitor the firm's compliance with its undertakings, adding that he hoped "this will enable our confidence to grow".
The decision will not affect any potential action taken by the Serious Fraud Office, although ministers said they were reassured that the firm would act quickly if any new information emerged from the continuing investigation.
G4S said it would now seek to bid for contracts where it had "proven expertise".
"Today's ministerial statement marks an important milestone in rebuilding our relationship with the UK government," its chief executive Ashley Almanza said.
"As part of our overall programme to strengthen the governance, management and performance of our UK government business we have consolidated central government contracts into a single business unit under new leadership and enhanced contract management processes."
The SFO is also scrutinising two G4S facility management contracts for UK courts. The firm has agreed to pay £4.5m to the Treasury for overcharging on these deals as part of its overall settlement.
The government also reached a £70.5m settlement with Serco this year over claims of overcharging on tagging contracts.